The spherical Fourier-Bessel (SFB) decomposition is a natural choice for the radial/angular separation that allows optimal extraction of cosmological information from large volume galaxy surveys. In this paper we develop a SFB power spectrum estimato
r that allows the measurement of the largest angular and radial modes with the next generation of galaxy surveys. The code measures the pseudo-SFB power spectrum, and takes into account mask, selection function, pixel window, and shot noise. We show that the local average effect is significant only in the largest-scale mode, and we provide an analytical covariance matrix. By imposing boundary conditions at the minimum and maximum radius encompassing the survey volume, the estimator does not suffer from the numerical instabilities that have proven challenging in the past. The estimator is demonstrated on simplified Roman-like, SPHEREx-like, and Euclid-like mask and selection functions. For intuition and validation, we also explore the SFB power spectrum in the Limber approximation. We release the associated public code written in Julia.
Future high spectroscopic resolution galaxy surveys will observe galaxies with nearly full-sky footprints. Modeling the galaxy clustering for these surveys, therefore, must include the wide-angle effect with narrow redshift binning. In particular, wh
en the redshift-bin size is comparable to the typical peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect becomes important. A naive projection of the Fourier-space RSD model to spherical harmonic space leads to diverging expressions. In this paper we present a general formalism of projecting the higher-order RSD terms into spherical harmonic space. We show that the nonlinear RSD effect, including the fingers-of-God (FoG), can be entirely attributed to a modification of the radial window function. We find that while linear RSD enhances the harmonic-space power spectrum, unlike the three-dimensional case, the enhancement decreases on small angular-scales. The fingers-of-God suppress the angular power spectrum on all transverse scales if the bin size is smaller than $Delta r lesssim pi sigma_u$; for example, the radial bin sizes corresponding to a spectral resolution $R=lambda/Delta lambda$ of a few hundred satisfy the condition. We also provide the flat-sky approximation which reproduces the full calculation to sub-percent accuracy.
We present a fast implementation of the next-to-leading order (1-loop) redshift-space galaxy power spectrum by using FFTlog-based methods. [V. Desjacques, D. Jeong, and F. Schmidt, JCAP 1812 (12), 035] have shown that the 1-loop galaxy power spectrum
in redshift space can be computed with 28 independent loop integrals with 22 bias parameters. Analytical calculation of the angular part of the loop integrals leaves the radial part in the form of a spherical Bessel transformation that is ready to be integrated numerically by using the FFTLog transformation. We find that the original 28 loop integrals can be solved with a total of 85 unique FFTLog transformations, yet leading to a few orders of magnitude speed up over traditional multi-dimensional integration. The code used in this work is publicly available at https://github.com/JosephTomlinson/GeneralBiasPk
The galaxy catalogs generated from low-resolution emission line surveys often contain both foreground and background interlopers due to line misidentification, which can bias the cosmological parameter estimation. In this paper, we present a method f
or correcting the interloper bias by using the joint-analysis of auto- and cross-power spectra of the main and the interloper samples. In particular, we can measure the interloper fractions from the cross-correlation between the interlopers and survey galaxies, because the true cross-correlation must be negligibly small. The estimated interloper fractions, in turn, remove the interloper bias in the cosmological parameter estimation. For example, in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) low-redshift ($z<0.5$) [O II] $lambda3727${AA} emitters contaminate high-redshift ($1.9<z<3.5$) Lyman-$alpha$ line emitters. We demonstrate that the joint-analysis method yields a high signal-to-noise ratio measurement of the interloper fractions while only marginally increasing the uncertainties in the cosmological parameters relative to the case without interlopers. We also show the same is true for the high-latitude spectroscopic survey of Wide-Field Infrared Survey Telescope (WFIRST) mission where contamination occurs between the Balmer-$alpha$ line emitters at lower redshifts ($1.1<z<1.9$) and Oxygen ([O III] $lambda5007${AA}) line emitters at higher redshifts ($1.7<z<2.8$).
We explore the possible spectrum of binary mergers of sub-solar mass black holes formed out of dark matter particles interacting via a dark electromagnetism. We estimate the properties of these dark black holes by assuming that their formation proces
s is parallel to Population-III star formation; except that dark molecular cooling can yield smaller opacity limit. We estimate the binary coalescence rates for the Advanced LIGO and Einstein telescope, and find that scenarios compatible with all current constraints could produce dark black holes at rates high enough for detection by Advanced LIGO.
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting
the galaxy power spectrum $P(k)$ onto the configuration space, $xi_ell^ u(r)$, or spherical harmonic space, $C_ell(chi,chi)$. First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.
We explore the evolution of the Stellar Mass-Star Formation Rate-Metallicity Relation using a set of 256 COSMOS and GOODS galaxies in the redshift range 1.90 < z < 2.35. We present the galaxies rest-frame optical emission-line fluxes derived from IR-
grism spectroscopy with the Hubble Space Telescope and combine these data with star formation rates and stellar masses obtained from deep, multi-wavelength (rest-frame UV to IR) photometry. We then compare these measurements to those for a local sample of galaxies carefully matched in stellar mass (7.5 < log(M*/Msol) < 10.5) and star formation rate (-0.5 < log(SFR) < 2.5 in Msol yr^-1). We find that the distribution of z ~ 2.1 galaxies in stellar mass-SFR-metallicity space is clearly different from that derived for our sample of similarly bright (L_Hb{eta} > 3 . 10^40 ergs s^-1) local galaxies, and this offset cannot be explained by simple systematic offsets in the derived quantities. At stellar masses above ~10^9 Msol and star formation rates above ~10 Msol yr^-1, the z ~ 2.1 galaxies have higher oxygen abundances than their local counterparts, while the opposite is true for lower-mass, lower-SFR systems.
